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<th>dwi2SH</th>
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<h2>Description</h2>
<p>
convert base diffusion-weighted images to their spherical harmonic representation.
</p>
<p>
This program outputs the spherical harmonic decomposition for the set measured signal attenuations. The signal attenuations are calculated by identifying the b-zero images from the diffusion encoding supplied (i.e. those with zero as the b-value), and dividing the remaining signals by the mean b-zero signal intensity. The spherical harmonic decomposition is then calculated by least-squares linear fitting.
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<p>
Note that this program makes use of implied symmetries in the diffusion profile. First, the fact the signal attenuation profile is real implies that it has conjugate symmetry, i.e. Y(l,-m) = Y(l,m)* (where * denotes the complex conjugate). Second, the diffusion profile should be antipodally symmetric (i.e. S(x) = S(-x)), implying that all odd l components should be zero. Therefore, this program only computes the even elements.
</p>
<p>
Note that the spherical harmonics equations used here differ slightly from those conventionally used, in that the (-1)^m factor has been omitted. This should be taken into account in all subsequent calculations.
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<p>
Each study in the output image corresponds to a different spherical harmonic component. Each study will correspond to the following:
</p>
<p>
study 0: l = 0, m = 0
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<p>
study 1: l = 2, m = 0
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<p>
study 2: l = 2, m = 1, real part
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<p>
study 3: l = 2, m = 1, imaginary part
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<p>
study 4: l = 2, m = 2, real part
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<p>
study 5: l = 2, m = 2, imaginary part
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<p>
etc...
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<p>

</p>
<p class=indented><strong>syntax:</strong> &nbsp; &nbsp; dwi2SH [ options ] dwi SH </p>
<h2>Arguments</h2>
<table class=args>
<tr><td><b>dwi</b></td>
<td>the input diffusion-weighted image.</td></tr>
<tr><td><b>SH</b></td>
<td>the output spherical harmonics coefficients image.</td></tr>
</table>
<h2>Options</h2>
<table class=args>
<tr><td><b>-grad</b>&nbsp;<i>encoding</i></td>
<td>specify the diffusion-weighted gradient scheme used in the acquisition. The program will normally attempt to use the encoding stored in image header.
<table class=opts>
<tr><td><i>encoding</i></td>
<td>the gradient encoding, supplied as a 4xN text file with each line is in the format [ X Y Z b ], where [ X Y Z ] describe the direction of the applied gradient, and b gives the b-value in units (1000 s/mm^2).</td></tr>
</table></td></tr>
<tr><td><b>-lmax</b>&nbsp;<i>order</i></td>
<td>set the maximum harmonic order for the output series. By default, the program will use the highest possible lmax given the number of diffusion-weighted images.
<table class=opts>
<tr><td><i>order</i></td>
<td>the maximum harmonic order to use.</td></tr>
</table></td></tr>
<tr><td><b>-normalise</b></td>
<td>normalise the DW signal to the b=0 image</td></tr>
<tr><td><b>-info</b></td>
<td>display information messages.</td></tr>
<tr><td><b>-quiet</b></td>
<td>do not display information messages or progress status.</td></tr>
<tr><td><b>-debug</b></td>
<td>display debugging messages.</td></tr>
<tr><td><b>-help</b></td>
<td>display this information page and exit.</td></tr>
<tr><td><b>-version</b></td>
<td>display version information and exit.</td></tr>
</table>
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